Depending on the disease and the efficacy of any "protection" used, criminal assault, almost certainly. It is possible that a rape charge could be brought, even in the case of consensual sex, if the healthy partner's consent was contingent upon disclosure of the disease. Also, in the case of AIDS, it is not inconceivable that an attempted murder charge could be brought by a particularly zealous prosecutor.

If the person with the disease knows they have the disease and that it is communicable through sex, they will have knowingly exposed their partner to potential harm. If they disclose the disease to their partner and the partner still consents to sex, that is one thing and a fair argument could be made that the partner assumed the risk of exposure. If, however, the disease is not disclosed (or much worse, the healthy partner asks and is lied to) there exists a frighteningly solid case for knowingly and intentionally harming the healthy partner, i.e. assault. If the healthy partner asks and is lied to, I would go so far as to argue that by asking, the healthy partner expressed that their consent to sex was strictly contingent upon the other partner being disease-free, and that subsequently their consent was flawed. That argument is the natural precursor to a rape charge. Finally, if the disease in question is AIDS, incurable and fatal in the vast majority of cases, I do not think that an attempted murder (or murder, if the healthy partner subsequently dies of it) charge is outside the realm of possibility.

This, of course, all depends on how zealous the prosecutor is, how much activity was taken to protect the healthy partner (disclosure, use of a condom or medication to reduce the communicability of the particular disease, efficacy of the protection used, etc.), and the net result to the healthy partner (if the healthy partner does not become infected, it will be much harder to get a jury to buy into a criminal charge).

I realize this does not strictly answer the question and that it is very general, but very few such cases have been filed, the fact patterns have been widely varied, and the results are "all over the map." The best answer is that a person who fails to disclose their STD to a partner cannot be certain that they will be immune from prosecution.